Solving Systems with an Inverse Matrix

Algebra Level 2

A system of equations is given by

\[\begin{align} ax + by &= 5 \\ cx + dy &= -1. \end{align} \]

If the inverse of \(\left[ \begin{array}{cc} a & b \\ c & d \end{array} \right]\) is \(\left[ \begin{array}{cc} 3 & 2 \\ -3 & 1 \end{array} \right]\), then what is \(x + y?\)

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